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Optimal ℓ 1 Rank One Matrix Decomposition

In: Harmonic Analysis and Applications

Author

Listed:
  • Radu Balan

    (University of Maryland)

  • Kasso A. Okoudjou

    (University of Maryland)

  • Michael Rawson

    (University of Maryland)

  • Yang Wang

    (Hong Kong University of Science and Technology)

  • Rui Zhang

    (Hong Kong University of Science and Technology)

Abstract

In this paper, we consider the decomposition of positive semidefinite matrices as a sum of rank one matrices. We introduce and investigate the properties of various measures of optimality of such decompositions. For some classes of positive semidefinite matrices, we give explicitly these optimal decompositions. These classes include diagonally dominant matrices and certain of their generalizations, 2 × 2, and a class of 3 × 3 matrices.

Suggested Citation

  • Radu Balan & Kasso A. Okoudjou & Michael Rawson & Yang Wang & Rui Zhang, 2021. "Optimal ℓ 1 Rank One Matrix Decomposition," Springer Optimization and Its Applications, in: Michael Th. Rassias (ed.), Harmonic Analysis and Applications, pages 21-41, Springer.
    • Handle: RePEc:spr:spochp:978-3-030-61887-2_2
    DOI: 10.1007/978-3-030-61887-2_2
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    Keywords

    Primary 45P05; 47B10; Secondary 42C15.;
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